This trophy is for defeating your Dad, Owl,
The fight itself can be pretty tough - probably one of the hardest fights in the game up to this point. As with everything in this game, the trick is to take your time and learn his combos. His posture meter depletes very quickly, so focus on damaging his health at the beginning of each phase and then trying for deflections after his health is at around 1/3.
The best opportunities for damage come after he throws his little bomb that prevents item use. Dodge to the right and run around behind him and you should be able to get a hit in without being debuffed. Luckily, he uses this move a lot.
The other move to look out for is two shuriken, followed by a leaping overhead smash. Again, dodge to the right immediately before the smash lands and you should have an opportunity for a couple of hits. Use Ichimonji to empty your posture bar here, if you're close to full.
Each time you hit him, quickly dodge backwards to avoid getting hit by his jump & throw shuriken/poison mist.
His second phase is mostly the same as the first - the only differences being his smoke bomb attack, which will make you lose lock-on, and the poison mist after his jump (instead of the shuriken)
Be patient, learn the timing for deflecting his sword combos and wait for those damage opportunities and you'll eventually take him down. Good luck!